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Current time:0:00Total duration:4:46

Multiplying 2 fractions: number line

Video transcript

in a previous video we saw that we could view 2/3 times 6 as whatever number is 2/3 of the way to 6 on the number line which we saw is 4 or another way to think about it is that 4 is 2/3 of 6 2/3 times 6 can be viewed as well what gets me if I how many do I have if I take 2/3 of 6 now what we want to do now is apply that same idea but 2 multiplying that a fraction times a whole number but a fraction times a fraction so let's say that we wanted to take 3/4 3/4 and multiply it by and multiply it by 1/2 and we know of course this is the exact same thing the order that we multiply doesn't matter this is the exact same thing as 1/2 times 3/4 1/2 times 3/4 so to imagine where this gets us let's draw ourselves a number line so let's this is 0 and I'll do it pretty large so that we have some space to work in so that's 0 and then that is 1 and of course our line could keep on going and let's first imagine 3/4 times 1/2 as 3/4 of the way to 1/2 so first let's plot 1/2 on our number line well 1/2 is literally halfway between 0 and 1 so that's 1/2 right over there and how do we think about 3/4 of the way to 1/2 well what we could do is think about well what's a fourth of 1/2 we could divide this part of the number line into four equal sections so that's two equal sections now that's four equal sections and while we're at it let's divide all of the halves into four equal sections so let's divide all of the halves into four equal sections so that's four sections and now let's do this one I'm drawing my best to draw them equal sections so I've taken each of the halves and I've made them into four equal sections so this this distance right over here this gets us or this point right over here is 1/4 of 1/2 but that's not what we care about we want to get to 3/4 of 1/2 so we want to get to 1/2 3/4 of have so this point right over here this is literally 3/4 3/4 times 1/2 and this is of course 1/2 year but what number is this we can now visualize it on the number line and let me do this in a new color we can now visualize it on the number line but what number is this actually well a big clue is is that well before we had the the section between 0 & 1 divided it into two equal sections when we only have to plot 1/2 but then we took each of those two equal sections and then split them into 4 more sections so each of these each of these we owe by doing that we now essentially have divided the section between 0 & 1 into 8 equal sections so each of these is actually 1/8 so this point right over here is 1/8 this is two eighths and then this is 3/8 and that's that's in line with what we've seen about multiplying fractions before this should be equal to 3 times 1 times 1 over 4 4 times 2 4 times 2 which is equal to 3/8 which is equal to 3/8 and everything that we're talking about this all so we don't get confused this is all referring to this point right over here on the number line this point right over here but what if we thought about it the other way around what if we thought about it as 1/2 of the way to 3/4 so we could divide the space between 0 & 1 into fourths let's do that so that is 1/4 2/4 3/4 so this right over here is the number 3/4 and we want to go half of the way to 3/4 well what is 1/2 of the way to 3/4 well we split this section into two equal sections so we could split right over there we could split right over here and we want to go exactly one of those sections 1/2 of 3/4 gets us once again right over here to this point 3/8 so either way you imagine it what you're essentially taking 3/4 of 1/2 or saying I'm going to go 3/4 of the way to 1/2 or you say I'm going to go 1/2 of the way to 3/4 either way hopefully it now makes conceptual sense you can visualize it and it makes numeric sense this is going to be equal to 3/8